NCERT Class XI Mathematics - Straight Lines - Solutions
© examsnet.com
Question : 2
Total: 74
The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.
Solution:
Since base of an equilateral triangle lies along y-axis.
So,B(0, a) and C(0, –a).
Let the third vertex be A(x, 0) (Since ΔABC is an
equilateral triangle and its base lies on y-axis)
|BC| = |AB| = |AC| = 2a
⇒√ ( x − 0 ) 2 + ( 0 − a ) 2
⇒x 2 + a 2 4 a 2 x 2 3 a 2 √ 3 a
∴ A =( √ 3 a , 0 ) ( − √ 3 a , 0 )
Hence vertices of triangle are (0, a), (0, –a), and( − √ 3 a , 0 ) ( √ 3 a , 0 )
So,B(0, a) and C(0, –a).
Let the third vertex be A(x, 0) (Since ΔABC is an
equilateral triangle and its base lies on y-axis)
|BC| = |AB| = |AC| = 2a
⇒
⇒
∴ A =
Hence vertices of triangle are (0, a), (0, –a), and
© examsnet.com
Go to Question: